End Behavior

Front

What is end behavior in the context of graphing functions?

Back

End behavior describes the behavior of the graph of a function as the input values (x) approach positive or negative infinity.

Front

How do you determine the end behavior of a polynomial function?

Back

The end behavior of a polynomial function is determined by the degree of the polynomial and the sign of the leading coefficient.

Front

What happens to the graph of a polynomial function with an even degree and a positive leading coefficient as x approaches infinity?

Back

As x → ∞, f(x) → ∞ and as x → -∞, f(x) → ∞.

Front

What happens to the graph of a polynomial function with an odd degree and a positive leading coefficient as x approaches infinity?

Back

As x → ∞, f(x) → ∞ and as x → -∞, f(x) → -∞.

Front

What happens to the graph of a polynomial function with an even degree and a negative leading coefficient as x approaches infinity?

Back

As x → ∞, f(x) → -∞ and as x → -∞, f(x) → -∞.

Front

What happens to the graph of a polynomial function with an odd degree and a negative leading coefficient as x approaches infinity?

Back

As x → ∞, f(x) → -∞ and as x → -∞, f(x) → ∞.

Front

Given the function f(x) = 2x^3 - 4x + 1, what is the end behavior?

Back

As x → ∞, f(x) → ∞ and as x → -∞, f(x) → -∞.

Front

What is the end behavior of the function f(x) = -x^4 + 3x^2?

Back

As x → ∞, f(x) → -∞ and as x → -∞, f(x) → -∞.

Front

For the function f(x) = x^2 + 5, what is the end behavior?

Back

As x → ∞, f(x) → ∞ and as x → -∞, f(x) → ∞.

Front

What does it mean if a function's end behavior approaches a constant value as x approaches infinity?

Back

It means that the function levels off and approaches a horizontal asymptote.